In this, the first of the five major categories of this course, the topics covered include:

Limits of functions (including one-sided limits)
• An intuitive understanding of the limiting process.
• Calculating limits using algebra.
• Estimating limits from graphs or tables of data.

Asymptotic and unbounded behavior
• Understanding asymptotes in terms of graphical behavior.
• Describing asymptotic behavior in terms of limits involving infinity.
• Comparing relative magnitudes of functions and their rates of change (for example,
contrasting exponential growth, polynomial growth, and logarithmic growth).

Continuity as a property of functions
• An intuitive understanding of continuity.  (The function values can be made as
close as desired by taking sufficiently close values of the domain.)
• Understanding continuity in terms of limits.
• Geometric understanding of graphs of continuous functions (Intermediate
Value Theorem and Extreme Value Theorem).

Collection Contents


Resources in this section listed by standard.
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Understand the concept of limit and estimate limits from graphs and tables of values.
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Find limits by direct substitution.
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Find limits of sums, differences, products, and quotients.
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Find one-sided limits.
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Find limits of rational functions that are undefined at a point.
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Find limits at positive or negative infinity.
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Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.
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Understand continuity in terms of limits and functional values.
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Decide if a function is continuous at a point using definition of continuity.
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Find the types of discontinuities of a function: Removable, Infinite, Jump.
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Understand and use the Intermediate Value Theorem on a function over a closed interval.
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Understand and apply the Extreme Value Theorem: If f is continuous over a closed interval, then f has a maximum and a minimum on the interval.
Member Rating
Curriki RatingC
'C' - Curriki rating

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